How Geometry Tames Disorder in Lattice Fracture

Abstract

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.

References in corpus (8)

• Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
• Deformation of crosslinked semiflexible polymer networks
• Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS
• From damage percolation to crack nucleation through finite size criticality
• A Thermodynamic Framework for Additive Manufacturing, using Amorphous Polymers, Capable of Predicting Residual Stress, Warpage and Shrinkage
• Role of disorder in the size-scaling of material strength
• Fracture Toughness and Maximum Stress in a Disordered Lattice System
• Architecting mechanisms of damage in topological metamaterials